V
主页
Localizing motives, algebraic KK-theory and refined negative cyclic homology
发布人
https://m.youtube.com/watch?v=tUMOOmwKXyA Abstract: I will explain some recent results on the universal localizing invariant of stable categories over some base ring k, commuting with filtered colimits. The target of this invariant is the category of localizing motives, denoted by Mot^loc_k. I will explain that Mot^loc_k, considered as a symmetric monoidal category, is rigid in the sense of Gaitsgory and Rozenblyum. Intuitively this means that Mot^loc_k "looks like an Ind-completion of a small symmetric monoidal category, in which every object is dualizable". In particular, Mot^loc_k is dualizable. Morally, the rigidity of the category Mot^loc_k means that it can be thought of as a category of quasi-coherent sheaves on a sufficiently nice stack. I will explain how the proof of rigidity allows to compute morphisms in Mot^loc_k. In particular, we will obtain the corepresentability results for TR and TC (topological cyclic homology), when restricted to connective E_1-rings. I will also outline another application of rigidity of Mot^loc_k: the construction of the refined negative cyclic homology and its variants, which contain much more information than the usual negative cyclic homology. If the base E_{\infty}-ring k is Z-linear (or at least complex oriented), the target of the refined HC^- is the category Nuc(k[[u]]), where u is a variable of cohomological degree 2.
打开封面
下载高清视频
观看高清视频
视频下载器
Alexander Efimov: Commutation of K-theory with certain inverse limits
BunG Seminar Talk XXXVIII: Akhil Mathew. Basics of derived algebraic geometry.
Alexander Efimov, Dualizable categories and localizing motives, Part IV
Alexander Efimov, Dualizable categories and localizing motives, Part V
Algebraic K-Theory and P-Adic Arithmetic Geometry - Matthew Morrow
Tasos Moulinos (Paris): Betti realizations of noncommutative motives
Pro-etale Cohomology of Rigid-Analytic Spaces - Johannes Anschütz
Alexander Efimov, Dualizable categories and localizing motives, Part II
Niels Feld (Toulouse): From motivic homotopy theory to birational geometry
Yves André - Motives and representation theory: principles and case studies
Peter Scholze - Analytic Prismatization
Maria Yakerson, Universality of algebraic K-theory
p-adic Hodge Theory for Analytic Varieties - Sally Gilles(IAS)
Geometric Langlands Seminar. Casimir Kothari: The Moduli Stack of Displays.
Atsushi Shiho - Weight Filtration on Log Crystalline Site
Alexaner Efimov: Localizing invariants of large categories: general theory.
Some Failures of Vanishing Theorems - Burt Totaro
Akhil Mathew, Introduction to dualisable categories and their K-theory, Part III
Thomas Nikolaus: (Generalized) Prismatic cohomology and the motivic filtration
David Loeffler - Iwasawa theory for Asai representations and the adjoint of a mo
K-theory in p-Adic Geometry - Greg Andreychev(IAS)
Akhil Mathew, Introduction to dualisable categories and their K-theory, Part IV
p-adic Hyperbolicity of Shimura Varieties - Xinwen Zhu
BunG Seminar. Talk XXVI.Justin Campbell: Hecke eigensheaves via chiral homology.
Akhil Mathew, Introduction to dualizable categories and their K-theory V
Johan de Jong - Integrality of the Betti Moduli Space
p-adic Non-Abelian Hodge Theory via Moduli Stacks - Ben Heuer
Geometric Langlands Seminar: Vladimir Drinfeld: The stacks of n-truncated BT II
Global conjecture: period and L-sheaves 1(Pavel Safronov)
David Ben-Zvi | The Langlands program via arithmetic QFT
Vasudevan- Finiteness Questions for Étale Coverings with Bdd Wild Ramification
XXXII:Kirill Magidson. Grothendieck-Lefschetz (GL1) and Gaitsgory-Lurie (GL2).
Igusa Stacks and Local-Global Compatibility - Mingjia Zhang 张明嘉
proof of the geometric Langlands conjecture 2(Gaitsgory)
Vladimir Drinfeld - Shimurian analogs of Barsotti-Tate groups.
Local and global conjectures on automorphic periods(Sug Woo Shin)
Juan Esteban Rodriguez Camargo: Analytic prismatization over Z_p, IV
Jacob Tsimerman - BSD and Estimates for Class Groups of Number Fields(Nekovar)
Tony Pantev - Birational and Singularity Invariants from nc Hodge Theory
On the K-theory of Z/p^n - Achim Krause